I haven't tried that yet, been raining cats and dogs here the last 2 days.
But I reckon because the DR Big is a big single cylinder, even though there will be some power loss, it shouldn't be so bad...

Bro, can you run your bike on reserve until the left tank is totally empty but the right tank is still 2/3 full?
If you can, it means the hose that links the 2 tanks is blocked. It's a simple matter...